Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
572 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#106×D53 | C2 | semidirect |
| 3. C2×#16810433 | C2 | semidirect |
| 4. #20276325 | C2 | semidirect |
| 5. #20272822 | C2 | semidirect |
| 6. #20272821 | C2 | semidirect |
| 7. C2×C53×#360 | C2 | semidirect |
| 12. #16810861 | C4 | semidirect |
| 13. #16810856 | C4 | semidirect |
| 49. #13133151 | C2×C4 | semidirect |
| 52. #13133149 | D4 | semidirect |
| 61. C2×Q16×C53 | C2×C4 | semidirect |
| 63. C2×D8×C53 | C2×C4 | semidirect |
| 70. #106×C53 | D4 | semidirect |
| 176. C2×D53 | #360 | semidirect |
| 189. C2×#360 | D53 | semidirect |
| 218. C53 | #13001 | semidirect |
| 226. C2×Q16 | C4×D53 | semidirect |
| 228. C2×D8 | C4×D53 | semidirect |
| 260. #106 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284292 | 2 |
| C2×#106×D53 | 2 |
| C2×#16810433 | 2 |
| #20276325 | 2 |
| #20272822 | 2 |
| #20272821 | 2 |
| C2×C53×#360 | 2 |
| #13001 | 53 |